Rewrite the power series so that its lower index of summation is n = 0.

Question

Rewrite the power series  so that its lower index of summation is n = 0.

Answer 1

it is the choice (n+1)x^(n-1)

look at problem this way, let k=n-1 so if n=1 then k=0. change the sum to k=0 to infinity

to adjust the terms notice that n=k+1, substitute for all n in the term, so now have sum k=0 to infinity

of (k+1)x(^k+1-2)=(k+1)x(^k-1), now let n=k and the sum is from n=0 to infinity of (n+1)x^(n-1).

if nervous about answer you can always check answer.

first two terms with n=1 start and nx^(n-2)are 1*x^-1, and 2*x⁰

first two terms with n=0 start and (n+1)x^(n-1) are 1*x^-1, and 2*x⁰